Math and Logic Puzzles: Redux

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Post Post #18  (isolation #0)  » Mon Apr 30, 2018 9:01 pm

Here's what should be easy ones, as was traditional for me last time:

You've been hired at the state prison and your job is to oversee the factory that makes the state's license plates. A new license plate series started on Monday, January 1, 2018. In the series, license plates have to be three letters followed by three digits. License plates cannot use the letters I or O, nor can the digits be all zeroes. The license plates are made in sequential order, with the very first plate made on the first day being AAA-001, the plate after that being AAA-002, and so on through AAA-999, with the plate following AAA-999 being AAB-001. Assume your prison makes exactly 25,000 plates per day Monday through Friday with no holiday breaks and that there are no other restrictions to the allowed plate numbers.
  1. What was the number of the last plate made on January 5, 2018? What will be the number of the last plate made on December 31, 2018?
  2. On what day will you make plate number ZZZ-999? Which plate that day will that be?*
  3. Suppose a law is passed that, after all the available numbers as above are exhausted, the alphabetic and numeric portions change places so that after ZZZ-999 comes 001-AAA. The numeric portion is still the portion that is incremented for the next plate, with the rollover from 999 to 001 incrementing the alphabetic portion, so the sequence goes ..., ZZZ-999, 001-AAA, 002-AAA, ..., 999-AAA, 001-AAB, ... If ZZZ-999 and 001-AAA are made the same day and you still make 25,000 plates total that day, when will you make plate number 999-ZZZ?
* For clarity, I'm looking for an ordinal number to the second part of the question, such as "the 12,345th plate" (which is incorrect, by the way).
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Post Post #22  (isolation #1)  » Tue May 01, 2018 9:46 am

brassherald is closer to the answer I get for the last plate on January 5, 2018 than Harambey180 is.
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Post Post #28  (isolation #2)  » Tue May 01, 2018 1:16 pm

I have the same answers as Harambey's new ones except for the date the prison makes 999-ZZZ. I'm at work on a short break, so I'm going to have a closer look at whether I'm the one who messed up after work.
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Post Post #29  (isolation #3)  » Tue May 01, 2018 3:23 pm

The error in the last date was mine, so Harambey180 has corrected all his mistakes.
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Post Post #30  (isolation #4)  » Wed May 02, 2018 7:01 am

Here's a logic puzzle:

You're a detective that has caught a serial thief. The thief had stolen a different item (a car, a phone, a ring, a TV, a wallet, and a watch) from a different person (Bradley, Eric, Jessica, Michelle, Richard, and Vivienne) each day from Monday through Saturday before you finally caught him on Sunday, before he could steal again. Your job now is to determine not only what items were stolen from each person, but also on what day each item was stolen. Your notes on the case so far are as follows:

1. Bradley was targeted on Thursday, Jessica was targeted on Friday, and Richard was not targeted on Saturday.
2. Michelle had her wallet stolen at some point after the thief stole from Bradley.
3. The watch was stolen on Wednesday, which is after the phone was stolen.
4. The thief stole from Vivienne and Eric in some order on consecutive days.
5. The ring was stolen from a woman three days before the TV was stolen from a man.

Can you solve the case?
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Post Post #32  (isolation #5)  » Wed May 02, 2018 9:48 am

That is correct :D
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Post Post #42  (isolation #6)  » Mon May 21, 2018 10:16 am

Let's breathe some new life into this:

Prove that no refactorable number is perfect. (A refactorable number is a number that is divisible by the number of divisors it has, including 1 and itself.)
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Post Post #44  (isolation #7)  » Mon May 21, 2018 12:32 pm

Looks good :)
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Post Post #61  (isolation #8)  » Fri Jun 29, 2018 1:00 pm

Never mind; I think I had too easy a question :P Let me think of a new one...
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Post Post #81  (isolation #9)  » Sun Jul 28, 2019 11:46 am

Here's an interesting one in addition to #76 above for those who like proofs: Prove that there are only finitely many triangular numbers that are also tetrahedral numbers. How many are there, and what are they?
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Post Post #88  (isolation #10)  » Sun Jul 28, 2019 6:21 pm

It only matters that both sides of the equation come out to the same number. You can use one variable on one side and another on the other.
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